Images of multilinear graded polynomials on upper triangular matrix algebras

Graded triangular algebras

Ela Graded Triangular Algebras

The structure of graded triangular algebras T of arbitrary dimension are studied in this paper. This is motivated in part for the important role that triangular algebras play in the study of oriented graphs, upper triangular matrix algebras or nest algebras. It is shown that T decomposes as T = U + ( ∑ i∈I Ti), where U is an R-submodule contained in the 0-homogeneous component and any Ti a well...

Involutions on graded matrix algebras

Graded Differential Geometry of Graded Matrix Algebras

We study the graded derivation-based noncommutative differential geometry of the Z2-graded algebra M(n|m) of complex (n+m)× (n+m)-matrices with the “usual block matrix grading” (for n 6= m). Beside the (infinite-dimensional) algebra of graded forms the graded Cartan calculus, graded symplectic structure, graded vector bundles, graded connections and curvature are introduced and investigated. In...

Derived Equivalent Mates of Triangular Matrix Algebras

A triangular matrix algebra over a field k is defined by a triplet (R, S, M) where R and S are k-algebras and RMS is an SR-bimodule. We show that if R, S and M are finite dimensional and the global dimensions of R and S are finite, then the triangular matrix algebra corresponding to (R, S, M) is derived equivalent to the one corresponding to (S, R, DM), where DM = Homk(M, k) is the dual of M , ...